MinT - Best Known (202−55, 202, s)-Nets in Base 4

Best Known (202−55, 202, s)-Nets in Base 4

(202−55, 202, 531)-Net over F₄ — Constructive and digital

Digital (147, 202, 531)-net over F₄, using

8 times m-reduction [i] based on digital (147, 210, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 70, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(202−55, 202, 1276)-Net over F₄ — Digital

Digital (147, 202, 1276)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−55, 202, 110459)-Net in Base 4 — Upper bound on s

There is no (147, 202, 110460)-net in base 4, because

1 times m-reduction [i] would yield (147, 201, 110460)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 331470 709976 256716 528276 238250 960438 841422 657492 612196 576683 209719 013347 845721 356781 473999 650300 203115 846946 703051 528673 > 4²⁰¹ [i]